package main

import "fmt"

/**
You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Note: Given n will be a positive integer.

Example 1:

Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps
Example 2:

Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

爬楼梯经典题目
*/
//递归实现
//func climbStairs(n int) int {
//	if n == 1 {
//		return 1
//	} else if n == 2 {
//		return 2
//	} else {
//		return climbStairs(n-1) + climbStairs(n-2)
//	}
//}

//动态规划迭代实现
func climbStairs(n int) int {
	if n == 1 {
		return 1
	}

	if n == 2 {
		return 2
	}

	prev, current := 1, 2

	for i := 3; i <= n; i++ {
		tmpcurrent := current
		tmpprev := prev

		current = tmpcurrent + tmpprev
		prev = tmpcurrent
	}

	return current
}

func main() {
	fmt.Println(climbStairs(44))
}
